{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter - 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-05T11:59:58.847557Z",
     "start_time": "2023-07-05T11:59:56.759736Z"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from scipy import stats\n",
    "import statsmodels.formula.api as smf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8. This question involves the use of simple linear regression on the Auto  data set.\n",
    "### (a) Use the lm() function to perform a simple linear regression with  mpg as the response and horsepower as the predictor. Use the  summary() function to print the results.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-05T11:59:58.848490Z",
     "start_time": "2023-07-05T11:59:56.934244Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(397, 9)\n"
     ]
    },
    {
     "data": {
      "text/plain": "    mpg  cylinders  displacement horsepower  weight  acceleration  year  \\\n0  18.0          8         307.0        130    3504          12.0    70   \n1  15.0          8         350.0        165    3693          11.5    70   \n2  18.0          8         318.0        150    3436          11.0    70   \n3  16.0          8         304.0        150    3433          12.0    70   \n4  17.0          8         302.0        140    3449          10.5    70   \n\n   origin                       name  \n0       1  chevrolet chevelle malibu  \n1       1          buick skylark 320  \n2       1         plymouth satellite  \n3       1              amc rebel sst  \n4       1                ford torino  ",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>mpg</th>\n      <th>cylinders</th>\n      <th>displacement</th>\n      <th>horsepower</th>\n      <th>weight</th>\n      <th>acceleration</th>\n      <th>year</th>\n      <th>origin</th>\n      <th>name</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>18.0</td>\n      <td>8</td>\n      <td>307.0</td>\n      <td>130</td>\n      <td>3504</td>\n      <td>12.0</td>\n      <td>70</td>\n      <td>1</td>\n      <td>chevrolet chevelle malibu</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>15.0</td>\n      <td>8</td>\n      <td>350.0</td>\n      <td>165</td>\n      <td>3693</td>\n      <td>11.5</td>\n      <td>70</td>\n      <td>1</td>\n      <td>buick skylark 320</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>18.0</td>\n      <td>8</td>\n      <td>318.0</td>\n      <td>150</td>\n      <td>3436</td>\n      <td>11.0</td>\n      <td>70</td>\n      <td>1</td>\n      <td>plymouth satellite</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>16.0</td>\n      <td>8</td>\n      <td>304.0</td>\n      <td>150</td>\n      <td>3433</td>\n      <td>12.0</td>\n      <td>70</td>\n      <td>1</td>\n      <td>amc rebel sst</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>17.0</td>\n      <td>8</td>\n      <td>302.0</td>\n      <td>140</td>\n      <td>3449</td>\n      <td>10.5</td>\n      <td>70</td>\n      <td>1</td>\n      <td>ford torino</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "auto = pd.read_csv(r'../data/Auto.csv')\n",
    "print(auto.shape)\n",
    "auto.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-05T11:59:58.848647Z",
     "start_time": "2023-07-05T11:59:56.949460Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "mpg             float64\ncylinders         int64\ndisplacement    float64\nhorsepower       object\nweight            int64\nacceleration    float64\nyear              int64\norigin            int64\nname             object\ndtype: object"
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "auto.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-05T11:59:58.848715Z",
     "start_time": "2023-07-05T11:59:56.952285Z"
    }
   },
   "outputs": [],
   "source": [
    "#horsepower is of type object, it needs to be int or float to be able to fit for regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-05T11:59:58.848817Z",
     "start_time": "2023-07-05T11:59:56.956416Z"
    }
   },
   "outputs": [],
   "source": [
    "auto['horsepower'] = auto['horsepower'].replace('?',np.nan)\n",
    "auto.dropna(inplace = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-05T11:59:58.848887Z",
     "start_time": "2023-07-05T11:59:56.960097Z"
    }
   },
   "outputs": [],
   "source": [
    "auto['horsepower'] = auto['horsepower'].astype('float')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-05T11:59:58.849024Z",
     "start_time": "2023-07-05T11:59:56.964042Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "mpg             float64\ncylinders         int64\ndisplacement    float64\nhorsepower      float64\nweight            int64\nacceleration    float64\nyear              int64\norigin            int64\nname             object\ndtype: object"
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "auto.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-05T11:59:58.849137Z",
     "start_time": "2023-07-05T11:59:56.972262Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    mpg   R-squared:                       0.606\n",
      "Model:                            OLS   Adj. R-squared:                  0.605\n",
      "Method:                 Least Squares   F-statistic:                     599.7\n",
      "Date:                Wed, 05 Jul 2023   Prob (F-statistic):           7.03e-81\n",
      "Time:                        19:59:56   Log-Likelihood:                -1178.7\n",
      "No. Observations:                 392   AIC:                             2361.\n",
      "Df Residuals:                     390   BIC:                             2369.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     39.9359      0.717     55.660      0.000      38.525      41.347\n",
      "horsepower    -0.1578      0.006    -24.489      0.000      -0.171      -0.145\n",
      "==============================================================================\n",
      "Omnibus:                       16.432   Durbin-Watson:                   0.920\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               17.305\n",
      "Skew:                           0.492   Prob(JB):                     0.000175\n",
      "Kurtosis:                       3.299   Cond. No.                         322.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "result = smf.ols('mpg ~ horsepower',data = auto).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### i. Is there a relationship between the predictor and the response?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-05T11:59:58.849195Z",
     "start_time": "2023-07-05T11:59:56.983968Z"
    }
   },
   "outputs": [],
   "source": [
    "# Since there is a non negative ceofficient, there is a realtionship between predictor and response"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ii. How strong is the relationship between the predictor and the response?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-05T11:59:58.849269Z",
     "start_time": "2023-07-05T11:59:56.986684Z"
    }
   },
   "outputs": [],
   "source": [
    "# we can meauser the overall fit by R2 value, since R2 value is 0.60, we say that 60% of invariability is \n",
    "# explained by the predictor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### iii. Is the relationship between the predictor and the response positive or negative?\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-05T11:59:58.849329Z",
     "start_time": "2023-07-05T11:59:56.989198Z"
    }
   },
   "outputs": [],
   "source": [
    "# the value of the coefficient is -0.1578, hence the relationship is negative."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### iv. What is the predicted mpg associated with a horsepower of 98? What are the associated 95 % confidence and prediction intervals ?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-05T11:59:58.849492Z",
     "start_time": "2023-07-05T11:59:56.993948Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jarvis/opt/anaconda3/envs/py39/lib/python3.9/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but LinearRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": "array([24.46707715])"
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# i am not sure about how to find prediction with a given confidence. For this question i am using a model, to train\n",
    "# and then predict an answer\n",
    "model = LinearRegression()\n",
    "model.fit(auto['horsepower'].to_frame(),auto['mpg'])\n",
    "model.predict(pd.Series([98]).to_frame())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-05T11:59:58.853626Z",
     "start_time": "2023-07-05T11:59:56.999497Z"
    }
   },
   "outputs": [],
   "source": [
    "# we are getting the answer as 24.46 ,but we can't be sure about the confidence in the prediction and the resulting range \n",
    "# of the confidence"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (b) Plot the response and the predictor. Use the abline() function to display the least squares regression line.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-05T11:59:58.999857Z",
     "start_time": "2023-07-05T11:59:57.002764Z"
    }
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "regplot() takes from 0 to 1 positional arguments but 2 were given",
     "output_type": "error",
     "traceback": [
      "\u001B[0;31m---------------------------------------------------------------------------\u001B[0m",
      "\u001B[0;31mTypeError\u001B[0m                                 Traceback (most recent call last)",
      "Cell \u001B[0;32mIn[14], line 2\u001B[0m\n\u001B[1;32m      1\u001B[0m plt\u001B[38;5;241m.\u001B[39mfigure(figsize \u001B[38;5;241m=\u001B[39m (\u001B[38;5;241m12\u001B[39m,\u001B[38;5;241m8\u001B[39m))\n\u001B[0;32m----> 2\u001B[0m \u001B[43msns\u001B[49m\u001B[38;5;241;43m.\u001B[39;49m\u001B[43mregplot\u001B[49m\u001B[43m(\u001B[49m\u001B[43mauto\u001B[49m\u001B[43m[\u001B[49m\u001B[38;5;124;43m'\u001B[39;49m\u001B[38;5;124;43mhorsepower\u001B[39;49m\u001B[38;5;124;43m'\u001B[39;49m\u001B[43m]\u001B[49m\u001B[43m,\u001B[49m\u001B[43mauto\u001B[49m\u001B[43m[\u001B[49m\u001B[38;5;124;43m'\u001B[39;49m\u001B[38;5;124;43mmpg\u001B[39;49m\u001B[38;5;124;43m'\u001B[39;49m\u001B[43m]\u001B[49m\u001B[43m)\u001B[49m\n",
      "\u001B[0;31mTypeError\u001B[0m: regplot() takes from 0 to 1 positional arguments but 2 were given"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 1200x800 with 0 Axes>"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (12,8))\n",
    "sns.regplot(auto['horsepower'],auto['mpg'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (c) Use the plot() function to produce diagnostic plots of the least squares regression fit. Comment on any problems you see with the fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.346006Z"
    }
   },
   "outputs": [],
   "source": [
    "# Diagnostic plots cnotains four types of plot, residual vs fitted,normal q-q, scale-location,residuals vs leverage\n",
    "# Here i am plotting the first two graphs\n",
    "# one can refer to the link below to get more information - "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://data.library.virginia.edu/diagnostic-plots/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.347878Z"
    }
   },
   "outputs": [],
   "source": [
    "#dist of residuals\n",
    "plt.figure(figsize = (12,8))\n",
    "plt.ylim(-20,20)\n",
    "sns.regplot(result.fittedvalues,result.resid, lowess=True)\n",
    "plt.axhline(y = 0,linewidth = 0.5,linestyle = 'dashed',color = 'black')\n",
    "plt.xlabel('Fitted Vales')\n",
    "plt.ylabel('Residuals')\n",
    "plt.title('Residual Plot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.349761Z"
    }
   },
   "outputs": [],
   "source": [
    "# the distribution has some kind of pattern"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.352849Z"
    }
   },
   "outputs": [],
   "source": [
    "# Q-Q plot\n",
    "ax = stats.probplot(result.resid, dist='norm', plot=plt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.355566Z"
    }
   },
   "outputs": [],
   "source": [
    "# the q-q polt is close to ideal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 9. This question involves the use of multiple linear regression on the Auto data set.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.357338Z"
    }
   },
   "outputs": [],
   "source": [
    "auto.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (a) Produce a scatterplot matrix which includes all of the variables in the data set.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.359169Z"
    }
   },
   "outputs": [],
   "source": [
    "for col in auto.iloc[:,1:8].columns:\n",
    "    sns.scatterplot(auto[col],auto['mpg'])\n",
    "    plt.title(col)\n",
    "    plt.xlabel(col)\n",
    "    plt.ylabel('mpg')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (b) Compute the matrix of correlations between the variables using the function cor(). You will need to exclude the name variable, cor() which is qualitative.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.360945Z"
    }
   },
   "outputs": [],
   "source": [
    "auto.iloc[:,:-1].corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.362689Z"
    }
   },
   "outputs": [],
   "source": [
    "sns.heatmap(auto.iloc[:,:-1].corr())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (c) Use the lm() function to perform a multiple linear regression with mpg as the response and all other variables except name as the predictors. Use the summary() function to print the results. Comment on the output.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false,
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.364371Z"
    }
   },
   "outputs": [],
   "source": [
    "predictors = ' + '.join(auto.columns.difference(['name','mpg']))\n",
    "result = smf.ols('mpg ~ {}'.format(predictors),data = auto).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### i. Is there a relationship between the predictors and the response?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.365749Z"
    }
   },
   "outputs": [],
   "source": [
    "# since we are having non zero ceoffiencts, there is a relationship between the predictors and response.\n",
    "# also the value of f statistic is quite high, which supports the claim."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ii. Which predictors appear to have a statistically significant relationship to the response?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.367173Z"
    }
   },
   "outputs": [],
   "source": [
    "# Origin,weight, year have very significan p value of 0, displacement also has a very low p value."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### iii. What does the coefficient for the year variable suggest?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.368752Z"
    }
   },
   "outputs": [],
   "source": [
    "# Coefficient of year is 0.7508. It means that if we increase the value of year by i unit, kepping all other predictors fixec,\n",
    "# we would expect 0.7508 increase in the response."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### d) Use the plot() function to produce diagnostic plots of the linear regression fit. Comment on any problems you see with the fit. Do the residual plots suggest any unusually large outliers?\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.370324Z"
    }
   },
   "outputs": [],
   "source": [
    "#diagnotis plot\n",
    "#dist of residuals\n",
    "plt.figure(figsize = (12,8))\n",
    "plt.ylim(-15,15)\n",
    "sns.regplot(result.fittedvalues,result.resid, lowess=True)\n",
    "plt.axhline(y = 0,linewidth = 0.5,linestyle = 'dashed',color = 'black')\n",
    "plt.xlabel('Fitted Vales')\n",
    "plt.ylabel('Residuals')\n",
    "plt.title('Residual Plot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.371910Z"
    }
   },
   "outputs": [],
   "source": [
    "# Q-Q plot\n",
    "ax = stats.probplot(result.resid, dist='norm', plot=plt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.373436Z"
    }
   },
   "outputs": [],
   "source": [
    "# in both of the graphs we can see some points in the uppwe right corner behaving as outliers\n",
    "# Q-Q plot is very colse to  the ideal, and the residuals distribution plot is also accetable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (e) Use the * and : symbols to fit linear regression models with interaction effects. Do any interactions appear to be statistically significant?\n",
    "\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.375028Z"
    }
   },
   "outputs": [],
   "source": [
    "predictors = ' + '.join(auto.columns.difference(['name','mpg']))\n",
    "result = smf.ols('mpg ~ {} + horsepower*cylinders + horsepower*year'.format(predictors),data = auto).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.376543Z"
    }
   },
   "outputs": [],
   "source": [
    "# we have added two tersms, horsepower*cyllinder and horsepower*year, for both of these the p values are significant\n",
    "# Adding the interaction terms has resulted in the increase of R2 value from 82.1 to 87.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (f) Try a few different transformations of the variables, such as log(X), √X, X2. Comment on your findings.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.378292Z"
    }
   },
   "outputs": [],
   "source": [
    "predictors = ' + '.join(auto.columns.difference(['name','mpg']))\n",
    "result = smf.ols('mpg ~ {} + horsepower*cylinders + np.power(horsepower,2)'.format(predictors),data = auto).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.379533Z"
    }
   },
   "outputs": [],
   "source": [
    "# we saw in the chapter how the scatterplot between horsepower and mpg hinted a non linear realtionship\n",
    "# by adding a new term which is horsepower**2, we saw an increase in R2 value increase from 82.1 to 86.3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10. This question should be answered using the Carseats data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.381067Z"
    }
   },
   "outputs": [],
   "source": [
    "data = pd.read_csv('E:\\programming\\dataset\\Into_to_statstical_learning\\Carseats.csv')\n",
    "print(data.shape)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.382522Z"
    }
   },
   "outputs": [],
   "source": [
    "shelveloc_mapping = {'Bad':0,'Good':1,'Medium':2}\n",
    "yes_no_mapping = {'Yes':1,'No':0}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.384085Z"
    }
   },
   "outputs": [],
   "source": [
    "data['ShelveLoc'] = data['ShelveLoc'].map(shelveloc_mapping)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.385608Z"
    }
   },
   "outputs": [],
   "source": [
    "data['Urban'] = data['Urban'].map(yes_no_mapping)\n",
    "data['US'] = data['US'].map(yes_no_mapping)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.387036Z"
    }
   },
   "outputs": [],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.388931Z"
    }
   },
   "outputs": [],
   "source": [
    "data.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.392165Z"
    }
   },
   "outputs": [],
   "source": [
    "# we now a complete quantative data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (a) Fit a multiple regression model to predict Sales using Price, Urban, and US."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.395303Z"
    }
   },
   "outputs": [],
   "source": [
    "result = smf.ols('Sales ~ Price + Urban + US',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (b) Provide an interpretation of each coefficient in the model. Be careful—some of the variables in the model are qualitative!\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.396633Z"
    }
   },
   "outputs": [],
   "source": [
    "# from the coeffiecents we can see that  the Price and Urban are negatively related to Sales, and US is positively related\n",
    "# Looking at the p values, Price and Us have significant p-values, but Urban has a very high p values ,and its \n",
    "# better that we exclude it from the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (c) Write out the model in equation form, being careful to handle the qualitative variables properly.\n"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Sales = 13.0435 - 0.545*Price - 0.0219*Urban + 1.2006*US\n",
    "# in the above equation, Urban takes values (0,1) and so does US"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (d) For which of the predictors can you reject the null hypothesis H0 : βj = 0?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.398131Z"
    }
   },
   "outputs": [],
   "source": [
    "# although all the predictors are having coefficients non zero, but since Urban has a high value, we will not use it as a \n",
    "# predictor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (e) On the basis of your response to the previous question, fit a smaller model that only uses the predictors for which there is evidence of association with the outcome.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.399603Z"
    }
   },
   "outputs": [],
   "source": [
    "result = smf.ols('Sales ~ Price + US',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (f) How well do the models in (a) and (e) fit the data?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.401456Z"
    }
   },
   "outputs": [],
   "source": [
    "# Removing the Urban from the first model, there is no change in the R2 value in the second model. Through this we can also \n",
    "# conclude that Urban has no say in the prediction of the response, hence its better to use the model with two predictors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (g) Using the model from (e), obtain 95 % confidence intervals for the coefficient(s).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.402593Z"
    }
   },
   "outputs": [],
   "source": [
    "# for 95% of confidence value we calculate the range of x +/- 2*stddev(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.403958Z"
    }
   },
   "outputs": [],
   "source": [
    "coeff_price = -0.0545\n",
    "std_price = 0.005\n",
    "range_price = [coeff_price - 2*std_price,coeff_price + 2*std_price]\n",
    "\n",
    "coeff_US = 1.1996\n",
    "std_US = 0.258\n",
    "range_US = [coeff_US - 2*std_US,coeff_US + 2*std_US]\n",
    "\n",
    "print('With 95% confidence the range for Price coefficient is ',range_price)\n",
    "print('With 95% confidence the range for US coefficent is ',range_US)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### (h) Is there evidence of outliers or high leverage observations in the model from (e)?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.408994Z"
    }
   },
   "outputs": [],
   "source": [
    "#dist of residuals\n",
    "plt.figure(figsize = (12,8))\n",
    "plt.ylim(-15,15)\n",
    "sns.regplot(result.fittedvalues,result.resid, lowess=True)\n",
    "plt.axhline(y = 0,linewidth = 0.5,linestyle = 'dashed',color = 'black')\n",
    "plt.xlabel('Fitted Vales')\n",
    "plt.ylabel('Residuals')\n",
    "plt.title('Residual Plot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.409985Z"
    }
   },
   "outputs": [],
   "source": [
    "#from the graph, we can see its a good fit, and there is no pattern"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 11. In this problem we will investigate the t-statistic for the null hypothesis H0 : β = 0 in simple linear regression without an intercept. To begin, we generate a predictor x and a response y as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.412432Z"
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(1)\n",
    "\n",
    "X = np.random.normal(size = 100)\n",
    "Y = 2*X + np.random.normal(size = 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.414252Z"
    }
   },
   "outputs": [],
   "source": [
    "data = pd.DataFrame({'X':X,'y':Y})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.417272Z"
    }
   },
   "outputs": [],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (a) Perform a simple linear regression of y onto x, without an intercept. Report the coefficient estimate βˆ, the standard error of this coefficient estimate, and the t-statistic and p-value associated with the null hypothesis H0 : β = 0.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.420260Z"
    }
   },
   "outputs": [],
   "source": [
    "result = smf.ols('y~X + 0',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.423131Z"
    }
   },
   "outputs": [],
   "source": [
    "# coefficient estimate is 2.1067, std_error is 0.106,value of t-statistic is 19.792. P value is significant.\n",
    "# Hence, we reject null hypothesis, and there is a realationship between predictor and response."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (b) Now perform a simple linear regression of x onto y without an intercept, and report the coefficient estimate, its standard error, and the corresponding t-statistic and p-values associated with the null hypothesis H0 : β = 0.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.426150Z"
    }
   },
   "outputs": [],
   "source": [
    "result = smf.ols('X~y + 0',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.428354Z"
    }
   },
   "outputs": [],
   "source": [
    "# Coef estimate is 0.3789, std_error is 0.019, value of t statistic is 19.792, and p value is significant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (c) What is the relationship between the results obtained in (a) and (b)?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.430752Z"
    }
   },
   "outputs": [],
   "source": [
    "# Alhtought the coeff estimates and their std_errors were different, the value of t - statistic was sama in both the cases"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (d)  Show algebraically, and confirm numerically in R, that the t-statistic can be written as\n",
    "(\n",
    "√n − 1)\n",
    "n\n",
    "i=1 xiyi\n",
    "\u0016(\n",
    "\n",
    "n\n",
    "i=1 x2\n",
    "i )(\n",
    "n\n",
    "i=1 y2\n",
    "i ) − (\n",
    "\n",
    "n\n",
    "i=1 xiyi )2"
   ]
  },
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lYghsY5Bx6j2HT0qdRgY9KG7gMMMZmWYr+8AxnJ6VLSuBFJaQySiRk+cdwSKlVQoAAAA4AFO4rC0cUhjTLEv3pFH1NJ50Z6HP0BNOwDkcOCQCMHHKkVJSATvQSAMkgAdzQABw6bkIYdsHrUEV0rpI7bUVG2khs07CJGuI0iaUklQobIGcg1Cso+xtIjfMw3E46Z/w/pTSAZHLE7MjSybl5OTjj8OOhB/Gl3Q+eqAFsnHLE9QSD9ODTYCyGNLlIfIQh+dx7fpTBefaGaOJGV1Gfm4Pbp60W6iuWlbKglSp9DTh1qBjqSgYwVXubnyGjHls+9scduCfp2ppXYh00vlR7yuRnnkDH1zSxSrKuVI464PSi2gEYmka8eLauxVBznnnp/Wmx3sb7gf3bCTZhyBnnGR+OR+FPlC4pu1BKkBHDKuHOM5OOPXv9cVaFS1YERzFt0SqxXc+Dj6E/wBKrTy+S3KyyfPtwrkH7u7P6VS1Bkx2AqoDncduWJx0z3pm1DYmcQqHCbsAAnOOlADhMUWEBDIHHzOg4H4UtrIzRrKxURyKHXJORkDjmnYCbzov+eif99Cl86P++v51NmO4edH/AHhUjKGQr0z3o2AbEgjBALHJzljmo/JQPJvk3Bjko2MU0xDAsLTArtCRjHHQn/638/pUccEEcLo04Luu1nDDJGSf6mnqBMi2yHcpUtnOeppxliJBIORyDsPH6UtWGhXubi1275EVygOM7cj6ZpYJVAG4DceWYHPP4Z/yKdnYCbzg33Uc/wDAcfzoSRmJ3RMgHQnHP5GpsBLS496QyIHimyIkq7ZEVgDnDDNAgzS0DIpERG81bffIT1UDP5nFVbpI9QAg3So0bhyIpFDcHocHpmqXcQy9sZbiRWQPGDIjsRIBjacjjBz0/SrwE7AFXjx2+Un+tOTTQkRyRTKyylw7bhtXBAyePU9qiDedKp82MSHoBIMn/wAd5FCBj4ZBdBvKm3qO+Tj+lSLbSABRIoUDAADf/FUN2AGjjTaHflm2jC55/WmiGF8hZWO04IUAEH8BRcdhyLELg2/70sF3bi56fnUiiBuBkkHaRk8H3pO4aBC8TZaAK2RyQe47H86WKWR2LbSY2PByPl7EfmKLdwJZZPKheTGdozVWS5jEUReNRNNwgxuGe2TQkFx8KhSiCDMZUHfxwe+fX8KjQrmMStJucbhzgDjPb0piJJfIjaMFS29tuSScf5/rUgig3bdke70wM0tRlOaaJElZINsdsdzjAGT1H88/lVkXUeAp4kP8AOT0zTadguQvcOlzNGVDKke8KBy3+cGpEmFwoCEplc9RuXnkEfpSaAtDpRUjIKCaACigB1QCCQXjTB1KMoUqQc8Z/wAaadhNFJ2ubK4srcI90kjENIVJKDHUnp/nFaMMXkRLGGJVRgZpytYEK5JeNNpOWzkDgYHeoY4S/wBmmjYKqR7QpB749/ahOyAytNiWJb6KOR/ldnAQHcp2jj0JwRWxas8sPmSKoLgHA57Dv35zVVBIVrSLH7tRE24NuQAHIpsqW6SbnRt5wSVVjnB4zj6VF2UJJJa+ckkm5ZOi7srn/GnMkWSxt2JyCTkdQcjv609RCWgDSTOQwYSHliPYY47cCpbY7od2MBmYj6ZODQwRMQGBVgCpGCCOtIqIgCqoA9BSuMZLuS3ZYEG4LhVzimm3QypIfvKuztyP8ihOwhtvAYSckAZJCrwOcf4frU4RQchQCepAob1BEUdtFEHCJ8r9QTkGmvaK8nJxGFwEAxjt/WhSYWJdg3bioyOhxyKXAznHNIYtGaAIAeKM0ALRQAtKKQDqKAFFIiKmdoxk5P1oAojTiuqveiY4bkxgd9oHX8KvVUpXElYKWpGRXEJmVNrBSjhvmGRTZLQSMX8x0kZdpK9PyP4fkKq4EyIqkkAbj1IHWn0gFooASigBaKAENJQAtJQAlFAEA6UUALS0ALSg8UAMNzADgzRg+m4UvnRno4P0NFgAzoP7x+ik09HDqGGcHpkEH8jRYBxOBmmg0gAGl7UALnmlzTAAeaUHNIBaQHmgAJ5pM0wAGndRQAGmmgBRSGgBtG40AQ9qjmLqmU6/7uf6imgIr1Xa3VkDEqykqpIJGfalla5JRoQNhU7gR8wOOKrSwhs108EoVmXa4O3CkkHGeR6cGp53UIiP/GwAyODyOKVgIoJLgzOpiUIHKjAwcdQfp2p7/aCkm5cHaNnltn5sn/61DtcBbuJn8l0VmKOCQpxkfmPak2XEh8uXAUvkMnbBBHX6frRdWAs8hACcnuaQcVIxR1paBi0ZxQA4UcCgQb1H8Q/Om+bGD/rF/OiwCiSN2wrqxHYGnUAKKKAEpDQA0Hmnds0ANPWimBDRSAKgN7EqlisqqOSWjZQPxIppXAiN3bPKsioHcDgh1P8AX3/WpDdnAP2eU/hn+WarlFcct1IxwsJ/EMP5il33X/PP/wAdH/xVKyC7F3XLDG3b9cD/ABpAl13fP/Ax/wDE0e6Gou25DZBTnruYn+lOxP3eP/vk/wCNJ2AcFl7uv4L/APXoMbn/AJbuPoB/hQMURP8A895PyX/Cjyz/ABSufxAouAi2kQk8wmQt15lYj8s4px+z5T5EYv8Adwuc+/0p3bELE0MgJjUfKcH5cc07zIwSMgYOD9cZpagQXF15coROX+UlNpJKk4JH0qwjh1yM/iCKbWgD6KQwpCKQDccU4dKYBxSYpAQVVmklS7hRWUI5IOVz0GevrTjqJipdo0kiAFWQ87uAeccetMmLmzljnXgts3cYILYH6YzTSsA67nkhaJY2QFzgblyPxOaka7UOYwGDn7hI+U9Oh79f0NO1wH+bKqx5t3Zm4YIRhfzIponZrzywsqrgjJX5T9KmwDbW4aS3kbzFdlJ6kDA7ZxT4ZHuISeUYqeB0ByR9c8U2kBFCboW0O1SSD+8EhO7Ht7/pT7mNp7GRNp3spwrY6+lGlwFPnPHGYh5RB5R8cj04zUNxI8JjYbgzS7doOQVLdT+FNbgWozIsIDcuMgbm6+lQ+VPIYjMiER54D5yeMHp9aSsgY+JblGUOwkXfnIOCowePft+ftTliEE8KB2YCNgu7HH3eKLgMlt4VGyd2ZTIXQKDkE5z0+ppJ1MsLIoaTLZw6HgYx6U0xDZraSMwyeYXdHwMjnDOM/pkVdXINJu40OzzS0hhRQAlKOlABRigCqaY8KS7d4yV6c0IB+1SMEA/UVHc2y3UZQuy5BU4PUHrxRewD/IjITcits+6W5I/E0Nbq8yyNzt6DHelcLE1OpAJxQAqLhQAB0ApgLTSKQFK6haLyfJGVL4cvlzihiI59gtgikjbIEyD0z06d+TWnQksQCXywJgu8dwc5/Sph0qShRjFMmQsY3VcsjZx6joaFuBW1VJZbJVhjYyFgOD90dycU8NNAgxFmFIuxy4IHp3qtOWwupM6M0sZz8q5J56nGP6mpKkYUtACikNACGlFAB2ozSArUUAKKWgBaXtSAXtRQAUUAL1oNABTTzTAXnb70ozQAtLQAoPFFABSUAFFAC0UwEoFACmm0AVxS0gI450kZghPHqCM/T1qUU2rAOzxTXkWONnc4VRk8UrAO3gDJIxS5oAhmuPKYL5bMSpYYx26/zFJFe280nlpIC+M7SCCB9KfLpcLliqZu7lRzak/vCpweg7HgHtiiKT3BiLeTbcG1kLhjkAYG0cgjPrxx60Jfl7hohEwKplh3BzjHp+tVyIVyezmae2V5F2sc8Dp16/j1qxUvcYtFIAooAKQ9aAEBoJpgKKWgA7UUAIaTNAFcUtIDOj0+SKBUSYlgVJ5POB0z2GeaUWd7Ir+ZdBSwGNhPykdx9fTpxWnMibE0mmicYlmbaW3si8DPt6dP51DJppN1Cse5IUHJyDnjB6854FCmFh11p4Nt5cBcb+GIIPbIPPuB09TWiOAB6VEpXQ0rDuKaUTeGKqWHQ46VNxjgaXNABRTATvTgaADNLmgBM0ZoAXNIaAEFGaYC5ozQAuaM0ANpMUAQ5ozSAUU4dKAF3AEAnk9Kia5iU7TIpYfwg5P5UWAat3G/RZeTjmJh/SniVSrFeShII75oaC4lvcC4hEiqyg9N3f8A+tSrcRPI0YYb16qev1x6UW6BcFuI2YqHywGdvfH+TUgORQA6igAzRmgAzS5oAKSgBc4o7UAFJ3pgLSUAKPelNIQ2jNAyA0HO04IB7ZFNAVrF5Xs1Em7zAoBLIVOcehqa2Wdd3nOGycjkZH5AU3YSEnDrcLIqljsKrxkAkjr9cdaYkFyoiAkVURFGwDqf4s/h0oukgsSqkqyqzSllAIIxjrjH8j+dCx4E28g+YxJ9hgD+QpDK9pFDZL5SXOVAwIyV49+BnNPZrfzvN2P5mMbljbkfUCnq3cRHLub7OIVkPlsMsykHHTuPTP44qW2a48hVeP5lAUl25bjrxmnZWDqT7p/7kf8A32f8KMzf9Mx+ZqdBhib++n/fB/xo2y/89F/74/8Ar0aAAWUf8tF/FP8A69SIW2jdjd3xQwH0mR0zSAKWgBKWgAopgFFABRSArUZoAUdacKABmO07cZ7Z6VW84jIlu48noI1wf1JppAGUI589z9GGf5CgIuMraAH/AG8f/XpiHoZSvCxKP9ls/wBBSbpc5+0RAZxgJ3/OgB5RjjM7j6Af4UjRRhfnkfnjJcj+VK4D4pFJMYBVk/hbrjsfpUhZVGWIH1NDQxiTxSsyxyKxXGQpziqy3Eo1I27yR7du5Rjk+3WmkIskn7Sq78DYTt9f/wBX9ajjmlLbZYihDYz1DDHX25osgEN2UVt6jcjqp2nI+YgZ/wA+lK6PJKQHUPG25SVzwQRj/PtTtYC0KKgYClpgFFABSUgCjigCrmgGmAuaeDSArrHHNLN5iiQBwAG5A+UHp+NJHIRZNKWAwGI44UDtVCIoL4z2HmxsssyoHdF9+cfXrTkLzTwsxlikVWDKo+U8jjJH5fjTskBLF8t5MiqwTardOCSTnH5CqlymzT41YAS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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![37bd9870-c7df-4434-89cf-550bd53befe3.jpg](attachment:37bd9870-c7df-4434-89cf-550bd53befe3.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  (e) Using the results from (d), argue that the t-statistic for the regression of y onto x is the same as the t-statistic for the regression of x onto y.\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.437819Z"
    }
   },
   "outputs": [],
   "source": [
    "# The formula of t - statistic is symmetric for x and y, therefore if we interchange the values of x and y \n",
    "# we will get the same value of t - statistic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (f) In R, show that when regression is performed with an intercept, the t-statistic for H0 : β1 = 0 is the same for the regression of y onto x as it is for the regression of x onto y.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.448598Z"
    }
   },
   "outputs": [],
   "source": [
    "result = smf.ols('y~X',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.453317Z"
    }
   },
   "outputs": [],
   "source": [
    "result = smf.ols('X~y',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.456279Z"
    }
   },
   "outputs": [],
   "source": [
    "# t value is same  =19.783"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12. This problem involves simple linear regression without an intercept"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (a) Recall that the coefficient estimate βˆ for the linear regression of Y onto X without an intercept is given by (3.38). Under what circumstance is the coefficient estimate for the regression of X onto Y the same as the coefficient estimate for the regression of Y onto X?\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<-- insert picture here -->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (b) Generate an example in R with n = 100 observations in which the coefficient estimate for the regression of X onto Y is different from the coefficient estimate for the regression of Y onto X.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.460084Z"
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.464918Z"
    }
   },
   "outputs": [],
   "source": [
    "X = np.random.normal(size = 100)\n",
    "Y = 2*X + np.random.normal(size = 100)\n",
    "data = pd.DataFrame({'X':X,'y':Y})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.467053Z"
    }
   },
   "outputs": [],
   "source": [
    "lin_x_on_y = LinearRegression(fit_intercept=False)\n",
    "lin_x_on_y.fit(data['X'].to_frame(),data['y'])\n",
    "coef_1 = lin_x_on_y.coef_\n",
    "\n",
    "lin_y_on_x = LinearRegression(fit_intercept= False)\n",
    "lin_y_on_x.fit(data['y'].to_frame(),data['X'])\n",
    "coef_2 = lin_y_on_x.coef_\n",
    "\n",
    "print('coef_1 is {}, coef_2 is {}'.format(coef_1,coef_2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### c) Generate an example in R with n = 100 observations in which the coefficient estimate for the regression of X onto Y is the same as the coefficient estimate for the regression of Y onto X\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.468390Z"
    }
   },
   "outputs": [],
   "source": [
    "# we need to choose x and y in such a way that their variabce is same. \n",
    "X = np.random.normal(size = 100)\n",
    "y = np.random.permutation(X)\n",
    "data = pd.DataFrame({'X':X,'y':y})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.469705Z"
    }
   },
   "outputs": [],
   "source": [
    "lin_x_on_y = LinearRegression(fit_intercept=False)\n",
    "lin_x_on_y.fit(data['X'].to_frame(),data['y'])\n",
    "coef_1 = lin_x_on_y.coef_\n",
    "\n",
    "lin_y_on_x = LinearRegression(fit_intercept= False)\n",
    "lin_y_on_x.fit(data['y'].to_frame(),data['X'])\n",
    "coef_2 = lin_y_on_x.coef_\n",
    "\n",
    "print('coef_1 is {}, coef_2 is {}'.format(coef_1,coef_2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.470712Z"
    }
   },
   "outputs": [],
   "source": [
    "#both the coefficients are same"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 13. In this exercise you will create some simulated data and will fit simple linear regression models to it. Make sure to use set.seed(1) prior to starting part (a) to ensure consistent results.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (a) Using the rnorm() function, create a vector, x, containing 100 observations drawn from a N(0, 1) distribution. This represents a feature, X.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.472346Z"
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(1)\n",
    "X = np.random.normal(loc = 0,scale = 1,size = 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (b) Using the rnorm() function, create a vector, eps, containing 100 observations drawn from a N(0, 0.25) distribution\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.474516Z"
    }
   },
   "outputs": [],
   "source": [
    "eps = np.random.normal(loc = 0,scale = 0.25,size = 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (c) Using x and eps, generate a vector y according to the model\n",
    "### Y = −1+0.5X + eps\n",
    "### What is the length of the vector y? What are the values of β0 and β1 in this linear model?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.476572Z"
    }
   },
   "outputs": [],
   "source": [
    "Y = -1 + 0.5*X + eps\n",
    "print('length of y is ',Y.size)\n",
    "# beta0 = -1 , beta1 = 0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (d) Create a scatterplot displaying the relationship between x and y. Comment on what you observe.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.477784Z"
    }
   },
   "outputs": [],
   "source": [
    "plt.figure(figsize = (14,6))\n",
    "sns.scatterplot(Y,X)\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.title('Relationship b/w X and Y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (e) Fit a least squares linear model to predict y using x. Comment on the model obtained. How do βˆ0 and βˆ1 compare to β0 and β1?\n",
    " \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.478919Z"
    }
   },
   "outputs": [],
   "source": [
    "data = pd.DataFrame({'X':X,'y':Y})\n",
    "lin_model = LinearRegression(fit_intercept=True)\n",
    "lin_model.fit(data['X'].to_frame(),data['y'])\n",
    "\n",
    "print('estimated beta0 is ',lin_model.intercept_)\n",
    "print('estimated beta1 is ',lin_model.coef_[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.482242Z"
    }
   },
   "outputs": [],
   "source": [
    "# the estimated values are pretty similar to the true values\n",
    "# estimated ~ [-0.96,0.52]\n",
    "# true ~ [-1,0.5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (f) Display the least squares line on the scatterplot obtained in (d). Draw the population regression line on the plot, in a different color. Use the legend() command to create an appropriate legend\n",
    ".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.485924Z"
    }
   },
   "outputs": [],
   "source": [
    "tmp_x = np.linspace(data['X'].min(),data['X'].max(),100)\n",
    "tmp_y = -1 + 0.5*tmp_x\n",
    "\n",
    "plt.figure(figsize = (14,6))\n",
    "sns.scatterplot(X,Y)\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.plot(data['X'],lin_model.predict(data['X'].to_frame()),color = 'orange',label = 'Predicted Line')\n",
    "plt.title('Relationship b/w X and Y')\n",
    "plt.plot(tmp_x,tmp_y,color = 'green',label = 'True Line')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (g) Now fit a polynomial regression model that predicts y using x and x2. Is there evidence that the quadratic term improves the model fit? Explain your answer.\n",
    " \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.488799Z"
    }
   },
   "outputs": [],
   "source": [
    "# withoud x**2 term\n",
    "result = smf.ols('y~X',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.491290Z"
    }
   },
   "outputs": [],
   "source": [
    "# adding x**2 term\n",
    "result = smf.ols('y~X + np.power(X,2)',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.494654Z"
    }
   },
   "outputs": [],
   "source": [
    "# There is no change in R2 value, showing that adding the X**2 term has not benefited in predicting y.\n",
    "# also the p value is very high(0.856), hence, we cannot reject null hypothesis, and we conclude that y is not dependent on X**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (h) Repeat (a)–(f) after modifying the data generation process in such a way that there is less noise in the data. The model (3.39) should remain the same. You can do this by decreasing the variance of the normal distribution used to generate the error term  in (b). Describe your results.\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.498312Z"
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(1)\n",
    "X = np.random.normal(loc = 0,scale = 1,size = 100)\n",
    "\n",
    "eps = np.random.normal(loc = 0,scale = 0.01,size = 100)\n",
    "\n",
    "Y = -1 + 0.5*X + eps\n",
    "\n",
    "# beta0 = -1 , beta1 = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.503654Z"
    }
   },
   "outputs": [],
   "source": [
    "data = pd.DataFrame({'X':X,'y':Y})\n",
    "lin_model = LinearRegression(fit_intercept=True)\n",
    "lin_model.fit(data['X'].to_frame(),data['y'])\n",
    "\n",
    "beta_0_low =lin_model.intercept_\n",
    "beta_1_low = lin_model.coef_[0]\n",
    "\n",
    "print('For less noisy data - ')\n",
    "print('estimated beta0 is ',beta_0_low)\n",
    "print('estimated beta1 is ',beta_1_low)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.513533Z"
    }
   },
   "outputs": [],
   "source": [
    "# data with low noise\n",
    "sns.regplot(data['X'],data['y'])\n",
    "plt.title('Data with low noise')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.516920Z"
    }
   },
   "outputs": [],
   "source": [
    "result = smf.ols('y~X',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.520103Z"
    }
   },
   "outputs": [],
   "source": [
    "beta_0_std_low = 0.001\n",
    "beta_0_range_low = [beta_0_low - 2*beta_0_std_low,beta_0_low + 2*beta_0_std_low]\n",
    "\n",
    "beta_1_std_low = 0.001\n",
    "beta_1_range_low = [beta_1_low - 2*beta_1_std_low,beta_1_low + 2*beta_1_std_low]\n",
    "\n",
    "print('range for beta 0 for low noise data ',beta_0_range_low)\n",
    "print('range for beta 1 for low noise data ',beta_1_range_low)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.524584Z"
    }
   },
   "outputs": [],
   "source": [
    "# The estimated values of beta0 and beta1 are more closed to the actual value of beta0 and beta1\n",
    "# (-1,0.5) ~ (-0.998,0.500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (i) Repeat (a)–(f) after modifying the data generation process in such a way that there is more noise in the data. The model (3.39) should remain the same. You can do this by increasing the variance of the normal distribution used to generate the error term  in (b). Describe your results.\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.527696Z"
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(1)\n",
    "X = np.random.normal(loc = 0,scale = 1,size = 100)\n",
    "\n",
    "eps = np.random.normal(loc = 0,scale = 1,size = 100)\n",
    "\n",
    "Y = -1 + 0.5*X + eps\n",
    "\n",
    "# beta0 = -1 , beta1 = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.530500Z"
    }
   },
   "outputs": [],
   "source": [
    "data = pd.DataFrame({'X':X,'y':Y})\n",
    "lin_model = LinearRegression(fit_intercept=True)\n",
    "lin_model.fit(data['X'].to_frame(),data['y'])\n",
    "\n",
    "beta_0_high =lin_model.intercept_\n",
    "beta_1_high = lin_model.coef_[0]\n",
    "\n",
    "print('For more noisy data - ')\n",
    "print('estimated beta0 is ',lin_model.intercept_)\n",
    "print('estimated beta1 is ',lin_model.coef_[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.531804Z"
    }
   },
   "outputs": [],
   "source": [
    "sns.regplot(data['X'],data['y'])\n",
    "plt.plot('Data with high noise')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.532911Z"
    }
   },
   "outputs": [],
   "source": [
    "result = smf.ols('y~X',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.533935Z"
    }
   },
   "outputs": [],
   "source": [
    "beta_0_std_high = 0.094\n",
    "beta_0_range_high = [beta_0_high - 2*beta_0_std_high,beta_0_high + 2*beta_0_std_high]\n",
    "\n",
    "beta_1_std_high = 0.106\n",
    "beta_1_range_high = [beta_1_high - 2*beta_1_std_high,beta_1_high + 2*beta_1_std_high]\n",
    "\n",
    "print('range for beta 0 for high noise data ',beta_0_range_high)\n",
    "print('range for beta 1 for high noise data ',beta_1_range_high)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.534964Z"
    }
   },
   "outputs": [],
   "source": [
    "# We can see as we increase the noise the estimated values of beta0 and beta1 shift far away from the real values\n",
    "# estimated = (-0.852,0.594)\n",
    "# real = (-1,0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (j) What are the confidence intervals for β0 and β1 based on the original data set, the noisier data set, and the less noisy data set? Comment on your results.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.536032Z"
    }
   },
   "outputs": [],
   "source": [
    "print('range for beta 0 for low noise data ',beta_0_range_low)\n",
    "print('range for beta 1 for low noise data ',beta_1_range_low)\n",
    "print('')\n",
    "print('')\n",
    "print('range for beta 0 for high noise data ',beta_0_range_high)\n",
    "print('range for beta 1 for high noise data ',beta_1_range_high)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.537121Z"
    }
   },
   "outputs": [],
   "source": [
    "# For high noise data, the range is way more wide as compared to the low noise data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14. This problem focuses on the collinearity problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (a) Perform the following commands in R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.538216Z"
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(5)\n",
    "x1 = np.random.uniform(size = 100)\n",
    "x2 = 0.5*x1 + np.random.normal(size = 100) / 10\n",
    "y = 2 + 2*x1 + 0.3*x2 + np.random.normal(size = 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (b) What is the correlation between x1 and x2? Create a scatterplot displaying the relationship between the variables.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.539234Z"
    }
   },
   "outputs": [],
   "source": [
    "data = pd.DataFrame({'X1':x1,'X2':x2,'y':y})\n",
    "corr = data.corr()\n",
    "print(corr)\n",
    "sns.scatterplot(data['X1'],data['X2'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### c) Using this data, fit a least squares regression to predict y using x1 and x2. Describe the results obtained. What are βˆ0, βˆ1, and βˆ2? How do these relate to the true β0, β1, and β2? Can you reject the null hypothesis H0 : β1 = 0? How about the null hypothesis H0 : β2 = 0?\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.540319Z"
    }
   },
   "outputs": [],
   "source": [
    "result = smf.ols('y~X1 + X2',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.541346Z"
    }
   },
   "outputs": [],
   "source": [
    "tmp = pd.DataFrame({'beta0':[2,1.8158],'beta1':[2,2.0758],'beta2':[0.3,0.7584]}) \n",
    "tmp.index = ['True','Predicted']\n",
    "tmp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.542477Z"
    }
   },
   "outputs": [],
   "source": [
    "# since the predicted values for beta1  and beta2 are != 0. We reject the null hypothese for both the cases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (d) Now fit a least squares regression to predict y using only x1. Comment on your results. Can you reject the null hypothesis H0 : β1 = 0?\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.543588Z"
    }
   },
   "outputs": [],
   "source": [
    "result = smf.ols('y~X1',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.544584Z"
    }
   },
   "outputs": [],
   "source": [
    "# since beta1 != 0, we reject the null hypotheses, also p value is 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### e) Now fit a least squares regression to predict y using only x2. Comment on your results. Can you reject the null hypothesis H0 : β1 = 0?\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.545719Z"
    }
   },
   "outputs": [],
   "source": [
    "result = smf.ols('y~X2',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.547969Z"
    }
   },
   "outputs": [],
   "source": [
    "# we reject the null hypothses, as coef != 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (f) Do the results obtained in (c)–(e) contradict each other? Explain your answer.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.550027Z"
    }
   },
   "outputs": [],
   "source": [
    "# No, we can't say that the reults are contradicting each other. In the combined model in (c), the two predictors were \n",
    "# highly correlated, (that's how they were created, x2 is depencdent on x), and due to this collinearity effect, the \n",
    "# one of the predictors is not able to expain the results. While when we use separate models, there is no concept of collunearity."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (g) Now suppose we obtain one additional observation, which was unfortunately mismeasured.\n",
    "\n",
    "> x1=c(x1, 0.1)\n",
    "> x2=c(x2, 0.8)\n",
    "> y=c(y,6)\n",
    "### Re-fit the linear models from (c) to (e) using this new data. What effect does this new observation have on the each of the models? In each model, is this observation an outlier? A high-leverage point? Both? Explain your answers.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.551375Z"
    }
   },
   "outputs": [],
   "source": [
    "x1 = np.append(x1,0.1)\n",
    "x2 = np.append(x2,0.8)\n",
    "y = np.append(y,6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.552460Z"
    }
   },
   "outputs": [],
   "source": [
    "data = pd.DataFrame({'X1':x1,'X2':x2,'y':y})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.553575Z"
    }
   },
   "outputs": [],
   "source": [
    "# we can make a point here, that for x1, the value 0.1 is within the range of earlier value, however\n",
    "# for x2 and y, 0.8 and 6, respecively, are outliers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.554645Z"
    }
   },
   "outputs": [],
   "source": [
    "sns.scatterplot(data['X1'],data['X2'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.555788Z"
    }
   },
   "outputs": [],
   "source": [
    "# we can see the newly added data point is an outlier, is separately located from the others."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.556851Z"
    }
   },
   "outputs": [],
   "source": [
    "result = smf.ols('y~X1 + X2',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.558279Z"
    }
   },
   "outputs": [],
   "source": [
    "result = smf.ols('y~X1',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.559733Z"
    }
   },
   "outputs": [],
   "source": [
    "sns.regplot(data['X1'],data['y'])\n",
    "# in this case, the point is 'outlier, since it has a very high value of y'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.560990Z"
    }
   },
   "outputs": [],
   "source": [
    "result = smf.ols('y ~ X2',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.562138Z"
    }
   },
   "outputs": [],
   "source": [
    "sns.regplot(data['X2'],data['y'])\n",
    "# in this case, the righmost point tends to follow the general trend, but is far away from the distribtuion, \n",
    "# so, it is a high leverage point"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15. This problem involves the Boston data set, which we saw in the lab for this chapter. We will now try to predict per capita crime rate using the other variables in this data set. In other words, per capita crime rate is the response, and the other variables are the predictors\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.563747Z"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_boston\n",
    "\n",
    "boston_data = load_boston()\n",
    "data = pd.DataFrame(data = boston_data['data'],columns = boston_data['feature_names'])\n",
    "print(data.shape)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (a) For each predictor, fit a simple linear regression model to predict the response. Describe your results. In which of the models is there a statistically significant association between the predictor\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.564844Z"
    }
   },
   "outputs": [],
   "source": [
    "simple_coeff = []\n",
    "predictor = [col for col in data.columns if col != 'CRIM']\n",
    "for col in predictor:\n",
    "    result = smf.ols('CRIM ~ {}'.format(col),data = data).fit()\n",
    "    print('{}    {:.4f}  {:.4f}'.format(col,result.params[col],result.pvalues[col]))\n",
    "    simple_coeff.append(result.params[col])\n",
    "    sns.scatterplot(data[col],data['CRIM'])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.565937Z"
    }
   },
   "outputs": [],
   "source": [
    "# from aboce point, we can conclude that every predictor except CHAS, has a significant relation with CRIM."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (b) Fit a multiple regression model to predict the response using all of the predictors. Describe your results. For which predictors can we reject the null hypothesis H0 : βj = 0?\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.567026Z"
    }
   },
   "outputs": [],
   "source": [
    "sum_predictor = ' + '.join(predictor)\n",
    "result = smf.ols('CRIM ~ {}'.format(sum_predictor),data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.568035Z"
    }
   },
   "outputs": [],
   "source": [
    "# although the coeff are all non zero, but inspecting the p values, we can only reject null hypothesis of RAD,DIS and LSTAT"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (c) How do your results from (a) compare to your results from (b)? Create a plot displaying the univariate regression coefficients from (a) on the x-axis, and the multiple regression coefficients from (b) on the y-axis.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.569165Z"
    }
   },
   "outputs": [],
   "source": [
    "multi_coeff = [result.params[col] for col in predictor]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.570316Z"
    }
   },
   "outputs": [],
   "source": [
    "sns.scatterplot(simple_coeff,multi_coeff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.571712Z"
    }
   },
   "outputs": [],
   "source": [
    "#removing the outlier point for NOX\n",
    "simple_coeff.remove(31.24853120112292)\n",
    "multi_coeff.remove(-6.928835572793048)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.573071Z"
    }
   },
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "sns.scatterplot(simple_coeff,multi_coeff)\n",
    "\n",
    "lims = [\n",
    "    np.min([ax.get_xlim(), ax.get_ylim()]),  # min of both axes\n",
    "    np.max([ax.get_xlim(), ax.get_ylim()]),  # max of both axes\n",
    "]\n",
    "ax.plot(lims, lims, 'k-', alpha=0.75, zorder=0,color = 'orange')\n",
    "ax.set_aspect('equal')\n",
    "ax.set_xlim(lims)\n",
    "ax.set_ylim(lims)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (d) Is there evidence of non-linear association between any of the predictors and the response? To answer this question, for each predictor X, fit a model of the form\n",
    "Y = β0 + β1X + β2X2 + β3X3 + epsilon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.574137Z"
    }
   },
   "outputs": [],
   "source": [
    "for col in predictor:\n",
    "    print(col)\n",
    "    result = smf.ols('CRIM ~ {0} + np.power({0},2) + np.power({0},3)'.format(col),data = data).fit()\n",
    "    print(result.summary())\n",
    "    print()\n",
    "    print('--------------------------------------------------------------------------------------------')\n",
    "    print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2023-07-05T11:59:57.575989Z"
    }
   },
   "outputs": [],
   "source": []
  }
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